The overall modelling approach adopted is based on an assumption of quasi-steady flow. The numerical algorithm is based on a split-operator approach, in which the flow energy equation, sediment continuity equation, bed armoring, and bed material sorting processes are computed separately but iteratively within a computational time step. Linearization of the energy equation and subsequent substitution into the water continuity constraint at model junctions leads to a system of linear equations for the water-level changes at each node. Once this system is solved, the water levels, discharges, and sediment-transport, capacities at individual computational points are readily computed. The paper presents the essential details of the computational methods employed and describes limited application to a northern braided river.